Another topic of interest in graph theory is the notion of deletion-contraction. Many graph polynomials and invariants, including number of acyclic orientations [1]}, spanning trees and spanning forests, as well as a graph's chromatic and flow polynomials [2]}, satisfy a recursive formula relating a graph and the two graphs obtained by deleting and contracting an edge. The combinatorial and normalised Laplacian characteristic polynomials, however, are not known to satisfy a deletion-contraction recursion. The effects of edge deletion, contraction and related operations on combinatorial and normalised Laplacian eigenvalues are studied across [3]}, [4]}, [5]}.
